Phase diagram of two-color quark matter at nonzero baryon and isospin density

We investigate the properties of cold dense quark matter composed of two colors and two flavors of light quarks. In particular, we perform the first model calculation of the full phase diagram at nonzero baryon and isospin density, thus matching the model-independent predictions of chiral perturbation theory at low density to the conjectured phase structure at high density. We confirm the presence of the Fulde-Ferrell (FF) phase in the phase diagram and study its dependence on the tunable parameter in the Lagrangian that simulates the effects of the quantum axial anomaly. As a byproduct, we clarify the calculation of the thermodynamic potential in the presence of the FF pairing, which was previously based on an ad hoc subtraction of an unphysical cutoff artifact. Furthermore, we argue that close to the diquark (or pion) Bose-Einstein condensation transition, the system behaves as a dilute Bose gas so that our simple fermionic model in the mean-field approximation is not quantitatively adequate. We suggest that including thermal fluctuations of the order parameter for Bose-Einstein condensation is crucial for understanding available lattice data.Comment: 14 pages, REVTeX4-1, 7 eps figures; v2: minor modifications + references added; version to be published in Phys. Rev.

Linear sigma model at finite density in the 1/N expansion to next-to-leading order

We study relativistic Bose-Einstein condensation at finite density and temperature using the linear sigma model in the one-particle-irreducible 1/N-expansion. We derive the effective potential to next-to-leading (NLO) order and show that it can be renormalized in a temperature-independent manner. As a particular application, we study the thermodynamics of the pion gas in the chiral limit as well as with explicit symmetry breaking. At nonzero temperature we solve the NLO gap equation and show that the results describe the chiral-symmetry-restoring second-order phase transition in agreement with general universality arguments. However, due to nontrivial regularization issues, we are not able to extend the NLO analysis to nonzero chemical potential.Comment: 12 pages, REVTeX4, 6 eps figures; v2: added references + minor corrections throughout the text; version to appear in Phys. Rev.

Surface tension and the origin of the circular hydraulic jump in a thin liquid film

It was recently claimed by Bhagat et al. (J. Fluid Mech. vol. 851 (2018), R5) that the scientific literature on the circular hydraulic jump in a thin liquid film is flawed by improper treatment and severe underestimation of the influence of surface tension. Bhagat {\em et al.} use an energy equation with a new surface energy term that is introduced without reference, and they conclude that the location of the hydraulic jump is determined by surface tension alone. We show that this approach is incorrect and derive a corrected energy equation. Proper treatment of surface tension in thin film flows is of general interest beyond hydraulic jumps, and we show that the effect of surface tension is fully contained in the Laplace pressure due to the curvature of the surface. Following the same approach as Bhagat et al., i.e., keeping only the first derivative of the surface velocity, the influence of surface tension is, for thin films, much smaller than claimed by them. We further describe the influence of viscosity in thin film flows, and we conclude by discussing the distinction between time-dependent and stationary hydraulic jumps.Comment: 9 pages, 1 figur

Bubble Pinch-Off in a Rotating Flow

We create air bubbles at the tip of a “bathtub vortex” which reaches to a finite depth. The bathtub vortex is formed by letting water drain through a small hole at the bottom of a rotating cylindrical container. The tip of the needlelike surface dip is unstable at high rotation rates and releases bubbles which are carried down by the flow. Using high-speed imaging we find that the minimal neck radius of the unstable tip decreases in time as a power law with an exponent close to 1/3. This exponent was found by Gordillo et al. [Phys. Rev. Lett. 95, 194501 (2005)] to govern gas flow driven pinch-off, and indeed we find that the volume oscillations of the tip creates a considerable air flow through the neck. We argue that the Bernoulli pressure reduction caused by this air flow can become sufficient to overcome the centrifugal forces and cause the final pinch-off

Comment on Y. Couder and E. Fort: "Single-Particle Diffraction and Interference at a Macroscopic Scale", Phys. Rev. Lett. (2006)

In a paper from 2006, Couder and Fort [1] describe a version of the famous double slit experiment performed with drops bouncing on a vibrated fluid surface, where interference in the particle statistics is found even though it is possible to determine unambiguously which slit the "walking" drop passes. It is one of the first papers in an impressive series, showing that such walking drops closely resemble de Broglie waves and can reproduce typical quantum phenomena like tunneling and quantized states [2-13]. The double slit experiment is, however, a more stringent test of quantum mechanics, because it relies upon superposition and phase coherence. In the present comment we first point out that the experimental data presented in [1] are not convincing, and secondly we argue that it is not possible in general to capture quantum mechanical results in a system, where the trajectory of the particle is well-defined.Comment: 4 pages, 1 figur

Effective Lagrangians for quantum many-body systems

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